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In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum.
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics.It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.
A bosonic propagator is represented by a wavy line connecting two vertices (•~•). A fermionic propagator is represented by a solid line with an arrow connecting two vertices, (•←•). The number of vertices gives the order of the term in the perturbation series expansion of the transition amplitude.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
In some contexts in mathematical physics, the mappings F t, s are called propagation operators or simply propagators. In classical mechanics, the propagators are functions that operate on the phase space of a physical system. In quantum mechanics, the propagators are usually unitary operators on a Hilbert space. The propagators can be expressed ...
Common integrals in quantum field theory are all variations and generalizations of Gaussian integrals to the complex plane and to multiple dimensions. [ 1 ] : 13–15 Other integrals can be approximated by versions of the Gaussian integral.
Quantum mechanics describes the nature of atomic and subatomic systems using Schrödinger's wave equation. The classical limit of quantum mechanics and many formulations of quantum scattering use wave packets formed from various solutions to this equation. Quantum wave packet profiles change while propagating; they show dispersion.
The Källén–Lehmann spectral representation, or simply Lehmann representation, gives a general expression for the (time ordered) two-point function of an interacting quantum field theory as a sum of free propagators. It was discovered by Gunnar Källén in 1952, and independently by Harry Lehmann in 1954.